1. (a) Find the sum of all the integers between 1 and 1000 which are divisible by 7. (b) Hence, or otherwise, evaluate the sum of (7r+2) from r=1 to r=142

1a) 1000/7=142.8.... Therefore there are 142 multiples of 7 between 1 and 1000
Therefore the sum of series from 1 to 142 is 1/7th of the solution
Calculation:70.5142143=71071

1b) The sum of (7r+2) from r=1 to r=147 is equal to the sum of 7(the sum of (r) from r=1 to r=147) plus (the sum of (2) from r=1 to r=147)
Calculation:7(0.5142143) + 142*2 =71355